There are a number of applications where it is desirable to be able to identify an unknown location of an object which emits a signal. One example occurs when planning an indoor wireless local area network (LAN) having one or more RF or microwave emitters.
Of course precisely defining an object's location requires specifying coordinates in three dimensions (e.g., longitude, latitude, and altitude). In the discussion to follow, for simplicity of explanation it is assumed that the third coordinate (i.e., altitude) is either known or is otherwise easily determined once the other two coordinates (e.g., latitude and longitude) are identified. Those skilled in the art will be able to extrapolate the discussion to follow to the case where all three coordinates are to be determined.
There are a few known methods to locate signal emitters using a plurality of distributed sensors, or receivers, which are spaced apart from each other. Among the most common of these methods are: Time Difference of Arrival (TDOA), Time of Arrival (TOA), Angle of Arrival (AOA), and Received Signal Strength (RSS).
The TDOA method, also known sometimes as multilateration or hyperbolic positioning, is a process of locating an emitter by accurately computing the time difference of arrival (TDOA) of a signal emitted from the emitter to three or more sensors. In particular, if a signal is emitted from a signal emitter, it will arrive at slightly different times at two spatially separated sensor sites, the TDOA being due to the different distances to each sensor from the emitter. For given locations of the two sensors, there is a set of emitter locations that would give the same measurement of TDOA. Given two known sensor locations and a known TDOA between them, the locus of possible locations of the signal emitter lies on a hyperbola. In practice, the sensors are time synchronized and the difference in the time of arrival of a signal from a signal emitter at a pair of sensors is measured. With three or more sensors, multiple hyperbolas can be constructed from the TDOAs of different pairs of sensors. The location where the hyperbolas generated from the different sensor pairs intersect is the most likely location of the signal emitter.
In the TOA method, a signal emitter transmits a signal at a predetermined or known time. Three or more sensors each measure the arrival time of the signal at that sensor. The known time of arrival leads to circles of constant received time around each sensor. The locations where the circles from the three or more sensors intersect are the most likely location of the signal emitter.
In the AOA method, the angle of arrival of the signal is measured with special antennas at each receiver. This information is combined to help locate the signal emitter.
In the RSS method, the power of the received signal at each sensor is measured, and this information is combined to help locate the signal emitter. There are a few different emitter location procedures that employ RSS. For example, one commonly used method in planning indoor wireless LAN systems in a building of interest is to map the received signal strength at various locations around the building during a setup phase. From this map, a variety of algorithms can be used to locate the signal emitter based on computed received power at three or more sensors.
A more detailed explanation of principles employed in an RSS method of locating a signal emitter will now be provided, particularly illustrating a case involving an RF emitter and RF sensors.
FIG. 1 illustrates a general case of an RF emitter 110 and two RF sensors 122 and 124.
In free space, the received power of a signal transmitted by RF emitter 110 decreases with the square of the distance from RF emitter 110. For indoor or dense urban environments the power fall-off is even steeper, for example r−3 or r−4, where r is the distance from RF emitter 110. In general, given a transmitted power P0 measured at distance r0, the power P1 received at first RF sensor 122 is:
                                          P            1                    =                                                    P                0                            ⁡                              (                                                      r                    0                                                        r                    1                                                  )                                      n                          ,                            (        1        )            where r1 is the distance between RF emitter 110 and first RF sensor 122, and n is the exponential rate at which the power decreases with distance.
Likewise the received power P2 at second RF sensor 124 is:
                                          P            2                    =                                                    P                0                            ⁡                              (                                                      r                    0                                                        r                    2                                                  )                                      n                          ,                            (        2        )            where r2 is the distance between RF emitter 110 and second RF sensor 124.
This leads to:
                                          P            1                                P            2                          =                              (                                          r                2                                            r                1                                      )                    n                                    (        3        )            
With a bit of manipulation this yields:
                              10                      (                                          log                ⁡                                  (                                                            P                      1                                                              P                      2                                                        )                                            n                        )                          =                                                                        r                2                                            r                1                                                          =                      const            =            α                                              (        4        )            
It can be shown that this leads to a circle of a given radius and centered on the line defined by the two RF sensors. FIG. 2 illustrates an exemplary circle generated by power measurements of a signal transmitted by RF emitter 110 and received at RF sensors 122 and 124.
With at least three RF sensors, three such circles are generated, and the location of RF emitter 100 can be found where the three circles intercept. With many sensors, it is possible to increase the accuracy by determining the point where most of the generated circles intersect.
However, the addition of measurement uncertainty and noise makes this a difficult problem to solve analytically with a high degree of accuracy.
Moreover, using just the measured signal power, as it typical in most RSS methods, multiple emitters transmitting from different locations at the same time with the signals having the same characteristics (e.g., frequency, bandwidth, etc.) leads to confusing results for the emitter location.
Furthermore, with existing equipment, it is often difficult for a troubleshooter to easily and efficiently view all of the relevant data of interest to allow a clear picture of any coverage and interference issues. More robust data analysis and data presentation capabilities are needed. In particular, methods are needed that are robust when multiple emitters are present that transmit signals at the same time and on the same frequency.
What is needed, therefore, is a method and system for locating signal emitters that addresses one or more of these shortcomings.